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Polynomial preconditioned arnoldi with stability control

SIAM Journal on Scientific Computing

Embree, Mark; Loe, Jennifer A.; Morgan, Ronald

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. The GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level "double polynomial preconditioning"strategy provides an effective way to generate high-degree preconditioners.

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TYPE Journal Article YEAR 2021
DOIOSTIScopus

Towards Use of Mixed Precision in ECP Math Libraries [Exascale Computing Project]

Antz, Hartwig; Boman, Erik G.; Gates, Mark; Kruger, Scott; Li, Sherry; Loe, Jennifer A.; Osei-Kuffuor, Daniel; Tomov, Stan; Tsai, Yaohung M.; Meier Yang, Ulrike

The use of multiple types of precision in mathematical software has the potential to increase its performance on new heterogeneous architectures. The xSDK project focuses both on the investigation and development of multiprecision algorithms as well as their inclusion into xSDK member libraries. This report summarizes current efforts on including and/or using mixed precision capabilities in the math libraries Ginkgo, heFFTe, hypre, MAGMA, PETSc/TAO, SLATE, SuperLU, and Trilinos, including KokkosKernels. It contains both numerical results from libraries that already provide mixed precision capabilities, as well as descriptions of the strategies to incorporate multiprecision into established libraries.

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TYPE Other Report YEAR 2020
DOIOSTI
Results 26–41 of 41
Results 26–41 of 41